B1 and/or B0 mapping in MRI system using k-space spatial frequency domain filtering with complex pixel by pixel off-resonance phase in the B0 map

ABSTRACT

Frequency filtering of spatially modulated or “tagged” MRI data in the spatial frequency k-space domain with subsequent 2DFT to the spatial domain and pixel-by-pixel arithmetic calculations provide robust data that can be used to derive B1 and/or B0 maps for an MRI system.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation-in-part of copending application Ser.No. 12/382,605 filed Mar. 19, 2009, which is hereby incorporated byreference and from which priority rights are claimed under 35 U.S.C.§120.

FIELD

This application describes methods and apparatus for generatingmulti-dimensional maps of the spatial distribution of radio frequency(RF) magnetic fields (typically labelled as the “B1” field) and/or ofthe static magnetic field (typically labelled as the “B0” field) in MRI(magnetic resonance imaging) systems. Fast multi-dimensional mapping ofB1 and/or B0 is achieved by k-space processing of SPAMM taggingpatterns.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a general overall schematic depiction of an exemplary MRIsystem configured to practice the exemplary embodiments;

FIG. 2 is a schematic depiction of a pre-sequence to be employed inconjunction with a following MR imaging sequence so as to acquirespatially-tagged k-space data for use in the exemplary embodiments;

FIG. 3 is a schematic diagram, at a relatively high level, of exemplaryprocesses utilized in the exemplary embodiments for B1 mapping in an MRIsystem using k-space spatial frequency domain filtering;

FIG. 4 is a more detailed schematic flowchart of process control programcode structure that may be utilized in an exemplary embodiment of theMRI system shown in FIG. 1;

FIG. 5 is a schematic diagram of k-space filtering utilized in analternative embodiment;

FIG. 6 is also a schematic diagram of k-space frequency filteringutilized in an alternate embodiment;

FIG. 7 is a schematic diagram of an exemplary “phase cycling” embodimentutilizing first and second data acquisition cycles with differenttagging pre-pulse sequences followed by combination of the resultingk-space data sets so as to produce an improved “starting” k-space dataset;

FIG. 8 is an image of a human pelvis with visible spatial modulationtagging lines superimposed thereon from use of a pre-pulse taggingsequence;

FIG. 9 is a B1 map generated from the tagged image of FIG. 8;

FIG. 10 is a normalized B1 map from FIG. 9 with superimposed contourlines depicting variations in B1 effective magnitude across the humanpelvis;

FIGS. 11 a-11 f graphically depict pixel values across a line of imagedata illustrating how SPAMM tagging ultimately produces peak and valleyenvelope data needed for subsequent computation of B1 field values;

FIGS. 12 a-12 b graphically depict low-pass and bandpass demodulateddata;

FIGS. 13 a-13 c depict the generation of replicants in k-space generatedby partial amplitude modulation (e.g., SPAMM tagging);

FIG. 14 depicts exemplary processing of k-space data to produce a B1field map;

FIG. 15 depicts exemplary processing of k-space data to produce a B0field map;

FIGS. 16-17 provide exemplary B1 maps produced by the processesdescribed herein; and

FIG. 18 provides an exemplary B0 map produced by the processes describedherein.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

Magnetic resonance imaging (MRI) systems are by now well known and manydifferent types of commercially available MRI systems are regularlyemployed for medical research and/or diagnostic purposes. Although thereare many variations in detailed image acquisition processes and/or MRIsystem geometries, they all share some basic fundamental principles.

For example, MRI systems all utilize the principle of nuclear magneticresonance (NMR) wherein nuclei having a net magnetic moment (e.g.,nuclei having an odd number of protons or neutrons hydrogen nucleus) areimmersed in a static background magnetic field B0. Ideally, thisbackground static magnetic field is homogeneous throughout a volume tobe imaged (even in the presence of the intervening object to be imaged).This background magnetic field tends to align a significant number ofthe nuclei magnetic moments therewith so as to produce a rathersignificant net nuclei magnetization aligned with the homogeneousbackground magnetic field B0.

The nuclear magnetic moments can be thought of as rotating about an axisat a frequency which is proportional to the magnetic field imposed uponthe nucleus at its particular spatial location. The so-called Larmorangular frequency ω=γβ where γ is a gyromagnetic ratio constant for agiven species of nuclei and its structural environment and β is thestrength of the imposed magnetic field. Accordingly, in an ideal world,a particular species of nuclei having common physical surroundings wouldall have a common Larmor frequency of rotation. However, bysuperimposing an auxiliary magnetic field having a linear gradient(e.g., in one of three orthogonal directions x, y, z), it will beappreciated that the Larmor frequency of such common species of nucleidisposed along the changing field gradient will now have differentvalues in accordance with the magnitude of the linear magnetic gradientfield at the spatial location of a given nucleus. Again, in an idealworld, such superimposed magnetic gradient field would have only anexactly linear gradient in one desired dimension and would otherwise beuniform and homogeneous. Typically, an MRI system has three sets ofgradient coils arranged to impose linear magnetic gradient fields ineach of three different mutually orthogonal directions.

By transmitting an RF magnetic field at the Larmor frequency into thevolume that is to be imaged, one can selectively “excite” the nuclearmagnetic resonant (NMR) nuclei that happen to fall within a givenselected volume (e.g., a “slice”) so as to nutate the nuclear magneticmoment away from the nominal static magnetic field B0. Depending uponthe amplitude and duration of such an exciting RF pulse, the magneticmoment of a nucleus can be “nutated” away from the nominal B0 alignmentby controlled amounts (e.g., 90°). After such nutation, the nuclearmagnetic moment tends to relax back toward nominal alignment with B0,but with characteristic longitudinal and transverse time constants T1,T2 and, in the process, each relaxing nuclear magnetic moment emits aradio frequency response signal that can be detected as an RF signalhaving a particular amplitude, frequency and phase (e.g., relative tothe exciting RF field and/or to other NMR nuclei emitting RF responsesignals).

By carefully choosing a particular “MRI sequence” of RF excitationpulse(s) and magnetic gradient pulses, one can elicit meaningfulspatially-encoded RF response signals so as to permit construction of animage or map of the NMR nuclei densities throughout a specific volume ofthe MRI system (e.g., a slice of the “imaging volume”). Over the lastseveral decades of MRI system development, a very large number of MRIsequences have been discovered and commercialized. Since most, if notall, such imaging sequences can be utilized in the following exemplaryembodiments, and since such are already well known to those skilled inthe art, further detail about specific MRI sequences is not required.

The RF excitation fields transmitted into the imaging volume as well asthe RF response fields received from the imaging volume are transmittedand/or received via RF coils which act as RF antennae. Once again, thereare many different RF coil geometries well known to those in the art.For example, there may be “head” coils, “surface” coils, “whole body”coils, “multi-coil arrays” and the like. All of these RF antennae/coilstructures serve to transduce electromagnetic radio frequency fieldsto/from NMR nuclei in the imaging volume onto feed line(s) of the RFantennae/coils which are then connected appropriately to RF transmitterand/or receiver circuits (e.g., via a transmit/receive switch if thesame coil structure is used to both transmit and receive), as will beapparent to those skilled in the art.

Once again, in a perfect world, the RF antennae/coil sensitivitythroughout the volume to be imaged is desirably absolutely uniform andhomogeneous at all points within the volume to be imaged.

Unfortunately, the ideals of absolutely uniform homogeneity, absolutelylinear gradients, etc., desired for various magnetic/RF fields in theMRI system are not realized in practice. Accordingly, various “shimming”attempts are made to correct for unwanted departures from the idealand/or to compensate acquired signals that have been adversely affectedby such less than ideal circumstances.

This application is directed towards a new and improved technique formapping of the RF B1 magnetic field associated with transmit sensitivityof the RF antennae/coils of an MRI system and/or the static B0 magneticfield associated with the permanent magnet and/or other aspects of anMRI system that may affect the static B0 magnetic field. Various priortechniques have been used for generating such B1 maps which are thenused either to improve the design of the MRI system itself and/or toprovide compensated output images from the MRI system (e.g., especiallywhere quantitative measurements are to be made based upon such images).However, such prior techniques leave room for improvement—which theexemplary embodiments explained in detail below provide.

MRI requires both transmitted radio frequency (RF) fields and receivedradio frequency (RF) fields. These RF fields are often denoted as B1fields. The transmitted field, in typical usages, should beapproximately uniform over the area being imaged within the subject.Spatial inhomogeneities of the RF fields introduce unwanted effects,including various artifacts in images, degradations in image contrast,or degradation or failure of various quantification methods. Thetransmit field acting within human bodies exhibits greaternon-uniformity as main magnet field strength increases. The staticmagnetic main field is denoted as the B0 field. The effective B1 fieldsdepend both upon the engineering design of the MRI scanner (such as RFantenna/coil and magnet geometry), and the geometry and electromagneticproperties of the subject within the scanner (often a human patient).

Having information about the distribution of non-homogeneity in thetransmit B0 and B1 fields within a specific subject can be beneficial invarious ways. Advantages of having such data include being able tobetter interpret images and artifacts, being able to spatially improvethe actual field patterns by improved design of the scanner, being ableto interactively or dynamically refine the fields on specific subjectsand in specific scan areas, and being able to improve or correct theacquired data and/or resulting images. In some more advanced methods,such as “multichannel transmit” or “Transmit SENSE,” knowledge ofnon-uniform spatial field patterns is explicitly needed and explicitlyused to accomplish goals of improved RF excitation and spatiallocalization.

Numerous methods exist or have been proposed for experimentallydetermining the B1 field. When the information is determined orpresented in the form of a 2-D or 3-D spatial distribution, it is calleda B1 map.

A pulse sequence can be repeated several times using successiveamplitudes of RF excitation (i.e., nutation) pulses. The receive MRsignal intensity is known to have a certain functional dependence on theeffective B1 transmit amplitude, such as:S(θ(x,y,z),x,y,z)=[ρ(x,y,z)]*sin(θ(x,y,z))³  [Equation 1]θ(x,y,z)=RF_ampl_factor*(B1_spatial(x,y,z))  [Equation 2]where:

-   -   S is measured data (using a pulse sequence acquisition at the        scanner for various RF_ampl_factor values), and the unknown        value of B1_spatial (i.e., θ or B1_spatial) are the spatial        distribution(s) to be determined;    -   “S” denotes the MR signal intensity (the actual mathematical        functional dependence is based upon the pulse sequence used);    -   ρ is a signal strength factor such as the proton density, or a        proton density times the receive coil sensitivity, or the like;    -   RF_ampl_factor is an independently adjusted control factor        (e.g., RF pulse amplitude and duration) in the pulse sequence;    -   B1_spatial(x,y,z) is the form of a spatially dependent B1        associated with some reference value of the RF_ampl_factor; and    -   θ has the meaning of the spatially dependent effective B1 field.

The specific “S” formulae given above happen to be suitable for a pulsesequence producing a single stimulated echo with complete T1/TR signalrecovery, and minimal T1, T2 decay during the echo time, just as anexample.

In general, one detects or measures S, from which one can determine θ,from which one can determine B1_spatial. In the literature, sometimesauthors compute and report θ, and sometimes they compute and report B1.Converting from one to the other is simple, and the two terms may beused somewhat interchangeably throughout the following description.

To be rigorous, B1_spatial should represent an instantaneous physicalmeasurement of a component of a time-varying magnetic field. θ is thetime integral of (γB1), and γ is a gyromagnetic ratio. The time integralcan be a simple linear approximation or, more accurately, it can be theresult of integrating out the full Bloch equations. These relationshipsare well known in MRI, and are not discussed further here. Suffice it tosay, conversion between B1 and θ is straight-forward under typicalimaging conditions.

Multiple measurements are generally needed, so that from multiple valuesof S, it is possible to solve for “ρ” and θ.

Spatially localized images can be collected at a series of amplitudes.Analysis such as searching for a peak, or fitting a curve, can be doneto determine the strength of B1. In a simple exemplary case, such as astimulated echo sequence where S=S(θ)=sin(θ)³, if we assume anapproximately uniform B1_spatial(x,y,z), MR data can be collected ateach of several RF_ampl_factor values over some nominal range. TheRF_ampl_factor which yields the peak of the signal value “S” correspondsto θ(x,y,z)=π/2 (flip angle in radians), i.e., at the particularRF_ampl_factor for which S achieves a maximum,B1_spatial=(π/2)/RF_ampl_factor (once again, ignoring other factors suchas γ, the RF pulse duration, etc.).

Other pulse sequences can be used, and other features of the signalstrength function can be used, such as the first minimum of the signalfor a 180° excitation pulse sequence, or such as themost-negative-valued signal for a 180° inversion pulse followed by asign-sensitive readout.

The successive amplitudes can be controlled by stepping through a rangein a prescribed fashion, perhaps linear increments across some nominalrange, or by iterative search methods like bisection, etc.

The varying amplitude factor, RF_ampl_factor, can be altered and appliedto all RF transmit pulses in a sequence in unison or, alternately, oneor a few pulses can be modified, while others are kept constant. Forexample, in a spin echo pulse sequence with two nutation pulses (α1 andα2), the signal strength can have the form:S(α1,α2)=sin(α1)*(sin(0.50α2))²,in which case α1 and α2 may be varied together, or either one can bevaried independently.

When B1_spatial(x,y,z) is not treated as constant (i.e., spatiallyhomogeneous), a simple but slow technique is to acquire and generateentire 2-D or 3-D images for each of several RF gain factors, and thento analyze the sets of images pixel-by-pixel, to fit or search for anamplitude scaling at each pixel location. Note that while using searchalgorithms and data-dependent choice of RF_ampl_factor to try toconverge to some optimal condition may be a good strategy when B1 isspatially uniform, it is not as suitable when B1 is non-uniform. A valueof RF_ampl_factor which achieves a goal such as a signal null at onelocation will not simultaneously achieve nulls at other locations, forexample.

The resulting B1 strengths, or flip angles θ, are then collected andpresented or stored in the form of an image, known as a B1 map. It ispossible that the B1 value can be treated either as a magnitude or as acomplex value which also includes some phase value (relative to asuitable or arbitrary reference phase).

Many acquisition methods are known which can be used to determine B1.Basically, all MRI pulse sequences have dependencies on B1 transmitfields, but some have more favorable characteristics, such as nearlylinear dependencies over a range of transmit values, or such asdependencies which are uncoupled from other variables like the tissue T1and T2 parameters. Corresponding analysis methods also exist, often forspecific acquisition methods.

In some cases, a series of many RF pulse amplitudes are used insuccessive acquisitions. A feature such as a null or minimum in thesignal level can then indicate which RF pulse amplitude is the nearestmatch to a certain flip angle or a certain B1 strength, as previouslyexplained.

Determining θ from S may be done in any of a few ways. There can be someregression or fitting to yield both ρ and S (even though there may be noexplicit interest in ρ). There could be a simple search for a simplefeature of the signal curve such as a maximum or null. There are ways tocollect a few values of S, (perhaps something like S1 usingRF_ampl_factor=RF_ampl_factor1, and S2 using RF_ampl_factor=(2RF_ampl_factor1), then finding a closed form mathematical dependence ofθ on S1 and S2, especially where that closed-form dependence haseliminated other variables like ρ.

It is common to collect pairs of images acquired with different numbersof RF pulses, or different amplitudes, and then form ratios of theimages. The ratios cancel other factors contributing to image intensity,leaving terms which depend on the RF pulses. The signal ratios havedependencies upon the RF pulse amplitudes which can be computed andinverted.

We have previously described collecting data with a few values ofRF_ampl_factor, each using the same pulse sequence and the sameacquisition parameters (other than RF_ampl_factor). A variant of thisidea is to acquire instead two (or more) pulse sequences, two or moreechoes, or the like. In one example, the two basic pulse sequences couldbe different, and each has a different functional dependence of S on θ(e.g., one spin echo with a saturation or inversion pre-pulse, and asecond spin echo without the pre-pulse). In another example, two or moreechoes can be acquired in a single, more complicated, pulse sequence(e.g., a spin echo and a stimulated echo, or some kind of first RF echoand second RF echo). In yet another example, a pulse sequence can be runwith two sets of parameters, such as a short TR and a long TR, perhapsin an interleaved fashion.

It is known that RF tagging techniques (including “SPAMM”) depend uponRF amplitudes, and so they can be used for determining B1 spatialdependencies (B1 maps).

In SPAMM RF tagging, two or more similar RF tagging nutation pulses areapplied, and a pulsed gradient is applied in between them. The gradientcauses spatial “modulation patterns”. One simple pattern is a periodicset of parallel stripes, with each cycle showing a generally sinusoidalintensity pattern. A simple physical explanation is that the two RFpulses can have similar effects individually, but the gradient appliedafter the first pulse causes a spatially dependent phase factorassociated with the first RF tagging pulse. Then, depending upon thisphase factor, the two RF tagging pulses may “add constructively” or“cancel each other like a destructive interference”. Thus, a series ofstripes is generated, with bright untagged signal appearing at locationswhere the tagging pulses cancel each other, and with tagged reduced(dark) signal bands appearing in locations where the effects of the twoRF tagging pulses combine together constructively.

It is known that spatial tagging lines may appear as pairs of minimaunder certain conditions, and that the spatial separation of the pair ofminima could be used to determine B1. The conditions for favorableapplication of this acquisition method and analysis approach can includea total tagging excitation higher than 90° (perhaps between 110° and270°), magnitude image reconstruction, and image pixel resolution ofmultiple pixels across each full spatial cycle of the complicatedtagging pattern.

Suppose the two pulses each have some nominal amplitude at a particularlocation, each yielding (perhaps) 35° tip angle in some region. Thetagging portion of the acquisition sequence can then be described ashaving a total tagging RF nutation angle of 70°, which dictates thepercentage of signal suppression at a trough in that region.

If SPAMM acquisition is used with image-domain peak-and-trough detectionmethod, significant error can arise if a neighboring peak and trough areused together in a ratio, but they have other confounding effects, likemajor differences in ρ.

The B1 and B0 fields are both perturbed by the presence of thepatient/object in the image volume. Both are causes for MR pulsesequences performing non-ideally. Both can have bigger effects at higherfield strength, i.e., more artifact at 3 T than 1.5 T usually.

The term “B0” is here used in the currently popular manner to includestatic field error from the scanner (e.g., the static magnet),susceptibility-based error from the patient or, even more loosely, toinclude chemical shift such as off-resonance of fat relative to water.That is, a map of B0 variation can describe the off-resonance amount ofundesirable variation, without regard for the underlying sources of sucherror.

B0 maps can be presented in units such as ppm, or Hz, or unscaled, oreven in units such as a fraction of the fat-water resonance shift. At 3T with hydrogen MR, 1 ppm is about 128 Hz. Fat-water-shift is about 420Hz or 3.3 ppm. Conversion between units can be freely accomplished.

Some examples of uses for B0 map data are:

-   -   Shimming    -   Validating or evaluating results of shimming    -   Identifying sources of image degradation (e.g., whether fat        saturation procedures are progressively degrading or failing, to        better identify which means might yield improvements, etc.)    -   Corrections in quantitative imaging (e.g., if some calculations        are made to yield T1 maps)    -   Direct interpretation of underlying interesting physical        quantities (e.g., temperature, concentrations of exogenous        contrast media, etc.)    -   Corrections such as for spatial distortion and/or        misregistration in echo planar imaging (EPI)    -   Corrections in fat-water imaging such as some more advanced        “Dixon Method” variants.

One conventional method for creating a B0 map involves collecting fieldecho images, at two different TE values (i.e., other than for TE, thetwo MRI sequences should be identically matched). Then, the complexphase of each (x, y) image pixel is calculated and the phase differencesare calculated:PhaseDiff=PhaseImage(TE2)−PhaseImage(TE1).

This phase difference can be attributed to the extra time required foroff-resonance (ΔF) terms to act, and the ΔF deviation may be easilydetermined from the phase difference image because:PhaseDiff(x,y)=2π*(TE2−TE1)*ΔF(x,y).

Such phase differences may affect (or be affected by) many other sourcesof background phase, such as RX coil spatial phase pattern, someconcomitant gradients, some eddy currents, some motion or flow effects,etc. Maps of the phase differences ΔF can be made for many differentspatial imaging schemes, such as 2-D, 3-D, 2-D multislice, etc.

There are known practical advantages of subtracting two distinct images,two distinct acquisitions. Depending on “how sensitive” the acquisitionis, one may see many phase wraps or only a few phase wraps in a phasemap. This sensitivity comes basically from the choice of TE (if a singleimage is acquired), or else from the difference in TE (if two images arephase subtracted, sensitivity depends on TE2−TE1). For long TE fieldecho sensitivity (e.g., 15-30 msec), it may be sometimes permissible tocount only the number of full cycles. For short TE field echosensitivity (e.g., 2 msec), only the main value of phase map may beneeded, which may not need any phase unwrapping at all. Methods of phaseunwrapping and the relevance of phase unwrapping are well known in theart.

This application describes an improved way to determine spatial patternsand amplitudes of transmit RF B1 fields and/or static B0 fields in MRIsystems. When used in conjunction with suitable MRI acquisition pulsesequences, measurements of patterns are produced which will depend bothupon the design of the scanner and upon the subject. Thus, experimentalmeasurement and determination on individual patients is more suitablethan, say, theoretical calculations for a single patient or singlegeometric model. The technique can be especially advantageous at higherfield strengths, in bodies and abdomens, or in cases where acquisitionspeed is important, or where motion in the body can make measurementproblematic.

The current application describes an exemplary method for determining orcalculating B1 or B0 maps, from experimentally acquired MR data of asuitable kind. In particular, advantages can be realized in accuracy orpractical performance or speed when generating B1 or B0 maps, especiallyinside humans or moving, living subjects.

Sometimes transmit fields are denoted by Tx, or Tx B1, or the like, andbecause they can exhibit a certain polarity of circular polarization,they can also be denoted as B1⁺. Similarly, receive RF fields associatedwith samples and coils can be denoted as Rx, or Rx B1, or B1⁻, etc.

The exemplary embodiments to be described below generate a B1 map of RFB1 signal magnitude values in a MRI system by using an MRI system to:

-   -   acquire at least one two-dimensional set of B1 amplitude-tagged        MRI data signals in spatial frequency domain k-space from MR        nuclei within an imaged volume of the MRI system;    -   process such k-space data to produce at least two of three        sub-sets of frequency-filtered k-space data (e.g., a baseline        low frequency sub-set, and at least one of (a) a higher        positive-frequency sub-set and (b) a higher negative-frequency        sub-set, such higher frequency sub-sets including respectively        corresponding harmonic versions of the baseline sub-set);    -   separately transforming each of these at least two filtered        sub-sets to respectively corresponding spatial domain data sets        (e.g., a baseline magnitude set, and at least one of (a) a        positive harmonic magnitude set and (b) a negative harmonic        magnitude set);    -   arithmetically combining the baseline magnitude set with the        harmonic magnitude sets on a pixel-by-pixel basis to provide        upper and lower magnitude envelope data sets;    -   processing the upper and lower magnitude envelope data set        values on a pixel-by-pixel basis to generate a B1 map data value        based on an inverse function (e.g., trigonometric in the        exemplary embodiments where sinusoidal tagging is used) of a        value related to a ratio of the upper and lower pixel data        values at a given pixel location in the spatial domain; and    -   storing or displaying the B1 map data values for use in MRI        system design and/or correcting/compensating diagnostic MR        images taken by the MRI system (e.g., perhaps on a        patient-by-patient basis).

Further exemplary embodiments to be described below, generate a B0 mapof effective off-resonance values in a MRI system by using an MRI systemto further:

-   -   process the image-domain phase associated with preferably at        least one of the two sub-sets of higher frequency-filtered        k-space data (e.g., at least one of (a) a higher        positive-frequency sub-set, and (b) a higher negative-frequency        sub-set), to yield a B0 map;    -   store or display the B0 map data values for use in MRI system        design and/or correcting/compensating diagnostic MR images taken        by the MRI system (e.g., perhaps on a patient-by-patient basis).

Preferably, the acquisition of k-space data from MR nuclei is achievedby applying at least two RF excitation pulses with at least oneinterleaved magnetic gradient pulse in a pre-sequence before applying anMRI pulse sequence (e.g., one of the many conventional well known MRIpulse sequences) to elicit successive MR responses in the time domainwhich are then mapped to respectively corresponding positions of k-space(e.g., typically to provide successive, respectively corresponding,lines of a multi-dimensional set of k-space data in a spatial frequencydomain.)

There are also advantages to be had if the original k-space data set is(a) two-dimensionally Fourier transformed to the spatial domain, and (b)further two-dimensionally Fourier transformed back to the spatialfrequency domain k-space before further processing. This detour to thespatial domain and back again to k-space has been discovered to provideadvantages in that it may produce a more idealized k-space data set forB1 mapping purposes. For example, if the MRI system happens to usemultiple receiver coils with outputs that are combined to achievecomplete data acquisition and/or uses parallel imaging techniques and/oruses complex-conjugate filling of a part of a k-space, etc., thenexperience has shown that a more idealized “starting” k-space data set(for B1 mapping) results from detouring into the spatial domain and backagain into the spatial frequency domain.

The spatial-tagging pre-pulse sequence may also be of many differenttypes. For example, there are well known tagging sequences such as theSPAMM (spatial modulation of magnetization) sequence and/or the DANTE(delays alternating with nutation for tailored excitation) sequence.Such tagging sequences can produce sinusoidally varying spatialmodulation which permits trigonometric inverse functions to be used asin the exemplary embodiments. Other tagging sequences may producenon-sinusoidal modulation, thus necessitating use of alternate inversefunctions.

The acquisition of a “starting” k-space data set may also involvemultiple data acquisition cycles and combining of the resulting k-spacedata. For example, it has been found particularly suitable to acquire afirst set of k-space data using a first tagging pre-sequence of at leasttwo RF excitation pulses having the same sense of nutation angle andthen also acquiring a second set of k-space data using a second taggingsequence of at least two RF excitation pulses having different,alternating nutation angle senses. The two sets of thus acquired k-spacedata are then arithmetically combined to produce a combined set ofk-space data to be used as a “starting” k-space data set in subsequentsteps of an exemplary embodiment. As will be explained in more detailbelow, this multiple acquisition and combination of k-space data canitself result in favorable reduction of harmonic content for the“starting” k-space data set to be used thereafter in an exemplary B1mapping process.

Once a suitable “starting” k-space data set has been acquired (which maybe a single first-acquisition k-space data set without detours orfurther preliminary processing), then it is spatial frequency-filteredin k-space by extracting k-space data from different portions of thek-space spatial frequency data set. In particular, the baseline lowfrequency sub-set of k-space is extracted, as well as at least onehigher frequency harmonic-containing portion of k-space data (e.g.,extracted from two other adjoining areas of k-space such as a strip ofk-space located above the baseline strip and a strip of data locatedbelow the baseline in k-space). The extraction may be made with respectto strips or rectangular/square (or other shaped) windows in k-space(possibly having sharp or weight-shaped edges) so as to, in effect,perform a frequency-filtering function since the k-space data is alreadyin the spatial frequency domain.

The frequency-filtered k-space extract data is then two-dimensionallyFourier transformed so as to bring it to the spatial domain—thusproviding at least two sets of spatial domain data—where by using onlymagnitude values for each data point, one can effectively de-modulatethe harmonic higher frequency data and be left with “envelope”-definingsets of values—one representing a low-frequency component and onerepresenting higher frequency, demodulated components (e.g., locatedabove (and/or below) the baseline component in k-space).

If the magnitude values from all sets of resulting spatial domain dataare added on a pixel-by-pixel basis, this provides a map of the peak or“upper” signal magnitude envelope. Similarly, subtracting from thebaseline magnitude set, on a pixel-by-pixel basis, the harmonicmagnitude set(s) provides a map of trough or “lower” signal magnitudeenvelope values.

Once such minimum and maximum pixel values have been determined, then a“tag depth” ratio data set may be created on a pixel-by-pixel basiswhere, for example, each pixel is assigned a value of tag depth ratiodata TD=min/max where min is the lower magnitude data set value and maxis the upper magnitude data set value. One may then calculate the arccosof the tag depth ratio values (cos⁻¹ TD) on a pixel-by-pixel basis so asto provide a B1 map of effective tag nutation flip angles θ. Of course,once the effective nutation flip angles θ are known, then thecorresponding B1 magnetic field strengths may be calculated based onknown formulae to provide a B1 map of effective B1 magnetic fieldstrengths. Either the B1 map of effective nutation flip angles θ or theB1 map of effective field strengths B1 may, of course, be normalized byratioing such values with the nominal desired value of θ or B1 provide amap of normalized B1 field strengths and/or flip angles θ.

Any of these types of B1 maps may, of course, be displayed on a screenor printer for visual observation/use (e.g., in designing MRI systemchanges and/or quantifying MRI images, “correcting” or “compensating”such MRI images, etc.).

Some advantages of this exemplary embodiment are:

-   -   Compared to image-domain detection of peaks-and-troughs with        tagged data, the exemplary processes reduce or remove errors        from unequal baseline signals being used within a single ratio,        and in a single determination of B1 in a region.    -   The exemplary processes remove the need to fit the local pixel        data to determine the actual height of a peak, (or the actual        minima of a trough) when the location of the peak (or trough) is        not centered on a pixel. If uncorrected, this would normally        lead to underestimation of the signal level difference between        peaks and troughs and, therefore, would lead to a bias towards        underestimating the B1 level and the flip angle θ.    -   The exemplary processes remove the bias which could arise when        there is partial averaging of the tagging spatial profile within        a pixel of finite extent.    -   The exemplary processes are amenable to true single-shot        readout, as a way to get rid of inconsistencies from human        motion (e.g., temporal resolution of much less than 100 msecs        can be obtained).    -   The exemplary processes can be easily used in a breathhold, to        gain immunity against respiratory motion artifacts.    -   Since the main acquisition method can be changed to use various        pulse sequences, there can be a wide range of resolution and        sensitivity to MRI parameters, i.e., it is possible to choose a        sequence with higher spatial resolution, or better sensitivity,        or reduced sensitivity to motion.    -   The exemplary processes can be used in the presence of diverse        tissue types, including fat.    -   The exemplary processes can be fully automated, and do not        require secondary inputs such as T1 maps, or off resonance maps,        or estimates of T2 or T2*.    -   The exemplary processes have high dynamic range, even without        extending the usable signal analysis range beyond 90° total        tagging angle. For example, one acquisition can capture a range        of flip angles from 20° to 80°, i.e., a dynamic range of 4-to-1.    -   The exemplary processes have high immunity to noisy images, as a        result of good filtering.    -   The exemplary processes have the ability to get good spatial        resolution, if desired (maps of 32×32 or less are not unusual        with some other methods).    -   The exemplary processes allow higher resolution, in terms of tag        lines being potentially closer together, than in        image-domain-based analysis of the tag lines. Note that the        filtering step, or the step of generating an envelope of the        modulation part, will generally introduce a blurring or loss of        resolution in the B1 map, which is on the order of the spacing        of the tag lines. Thus, closer tag line spacing, such as three        pixels per tagging profile cycle, as opposed to, say, 5-10        pixels per cycle, can yield a higher resolution B1 map.

The goals addressed herein include providing a method to generate quickB1 and B0 maps for all human anatomies, phantoms, all coils, etc. SPAMMtagging generates nominally regularly spaced tag lines as saturations orinversions. In a partial saturation case using 1-1 binomial RF pulses,the tag spatial profile is sinusoidal. The amplitude of saturationdepends on the RF nutation or tip angle of the SPAMM tagging pulses. Inan inversion case, different tagging appearance is provided where thespacing of doublet lines depends on the RF tip angle of the taggingpulses. The PhaseDiff image may have successive bands or rings which canbe “unwrapped” to provide a continuous and unambiguous trace of phasedifference changes. That is, in effect, there may be an additional stepof “counting the rings” to determine how many extra complete cycles ofphase are involved. For example, an x, y, z pixel with a nominal 40degrees phase difference in the map might actually be located in aregion between the second and third set of “rings” or “bands”, so thatthe true accumulated phase difference could be (2*360)+40=760. Thisprocess is generally referred to as “phase unwrapping” and is well knownin the art.

Largely the same processing and data acquisition as used for B1 mappingmay be used to generate not only a B1 map, but also a B0 map.

The described processing herein for B1 mapping separates out somek-space data from different spatial frequency regions (e.g., windowedareas in k-space) having similarities (e.g., harmonic content). One aptdescriptive term here adopted for the signals residing in such portionsof k-space is “replicants”. Such replicants are used to determine theamplitude associated with the modulated (i.e., tagged) part of an image.In the B1 mapping process, the magnitudes and ratios of magnitudes areused to infer the amount of tagging, and hence the strength of the B1fields which generated the tagged data.

It has now been discovered that an enhancement can also yield B0 maps.In particular, the B1 mapping process uses “windowed” replicants (e.g.,taken from a central k-space lobe, a right-side k-space lobe and aleft-side k-space lobe).

Now the same k-space replicants (lobes) can be used to produce a B0 map.For example, a 2DFT of the central lobe is calculated and a 2DFT of theright and/or left lobe(s) (when effectively shifted to the center ofk-space) can be calculated to produce two spatial domain images ofcomplex-valued pixels. Thereafter, there are several optional ways tocalculate B0 on a pixel-by-pixel basis:

-   -   (1a) take complex phase of central lobe and subtract it from        complex phase of shifted right lobe; or    -   (1b) use subtracted replicant phase, φtotal=(φright lobe−Φleft        lobe)/2; and    -   (2) convert phase to ΔF, which is proportional to ΔB0.

If the k-space data used in this process was derived byback-transforming (2DFT⁻¹) of a magnitude image, then there is noadvantage to using both right and left lobe replicants because theywould contain identical information. However, if the originally acquiredcomplex k-space data is used, the right and left lobes may vary, andcombining data from both lobes and stripping off phase data from thecentral lobe may offer a possible improvement in S/N ratio and/or inartifact removal.

To describe the B0 map generation in a more mathematical notation, aseries of values can be generated in succession, which for convenienceare simply named S1, S2, S3, etc.

Suppose the untagged image is represented in the image domain asS1=M*exp(iψ)where M is the real-valued magnitude as a function of position, i.e.,M(x,y) and where ψ is a real-valued phase term, also a function ofposition, i.e., ψ(x,y).

Then represent the corresponding k-space values asS2=F(S1)=m*exp(iφ)where m and φ are functions of (k_(x), k_(y)), and where F represents aFourier transform, such as a 2-dimensional discrete Fourier transform.

Then, with a spatial tagging profileP=(1−f)+f*cos(θ)use the accumulated phase between the two RF pulses of the SPAMMpre-pulseθ=k _(x) *x+gamma*ΔB0*twhere ΔB0 is the spatially varying off-resonance, where f is thespatially varying tag depth, where t is time separation between thecenters of the square RF pulses, and where gamma is the gyromagneticratio. Here, the term (k_(x)*x) shows the evolution of phase explicitlydue to the SPAMM pre-pulse gradient lobe between the SPAMM RF pulses.The term (gamma*ΔB0*t) shows other sources of phase accrual, which maybe thought of as off-resonance, as background B0 terms, assusceptibility terms, and the like. We need to solve for ΔB0, at leastapproximately.

Use the standard mathematical formulacos(θ)=(exp(iθ)+exp(−iθ))/2to write the tagged imageS3=P*S1,asS3=Mexp(iφ)((1−f)+f/2*exp(i(k_(x)*x+gamma ΔB0t))+f/2*exp(−i(k_(x)*x+gamma ΔB0t))).

Then the k-space of the partially saturated tagged image isS4=F(S3).

Assuming that the Fourier transforms of M exp(iφ), f and (ΔB0 t γ) areall functions that have their signal energy tightly localized near thecenter of k-space, then we have the three windowed regions of k-spaceS5=left window(S4)S6=center window(S4)S7=right window(S4)which are approximately equal toS5≈(m*exp(iφ))#(F(f/2))#(F(exp(i(k _(x) x+gamma ΔB0t))))S6≈(m*exp(iφ))#(F(i−f))S7≈(m*exp(iφ))#(F(f/2))#(F(exp(−i(k _(x) x+gamma ΔB0 t))))where # indicates the convolution operation.

Next, shift the left windowed and right windowed parts of k-space:S8=shift(S5)S8≈(m*exp(iφ))#(F(f/2))#(F(exp(i gamma ΔB0 t)))S9=shift(S7)S9≈(m*exp(iφ))#(F(f/2))#(F(exp(−i gamma ΔB0 t))).

Next, perform a Fourier transform, such as an inverse 2-D discreteFourier transform, on the shifted windowed k-space partsS10=F(S8)S10≈M exp(iψ)*f/2*exp(i gamma ΔB0 t)S11=F(S9)S11≈M exp(iψ)*f/2*exp(−i gamma ΔB0 t).

Next, take the phase angles of these complex imagesS12=arg(S10)S12≈ψ+gamma ΔB0 tS13=arg(S11)S13≈ψ−gamma ΔB0 t.

Finally, take the difference of the phase maps, and solve for ΔB0S14=S13−S12S14≈2ΔB0 t γΔB0=S14/(2 gamma t).

The MRI system shown in FIG. 1 includes a gantry 10 (shown in schematiccross-section) and various related system components 20 interfacedtherewith. At least the gantry 10 is typically located in a shieldedroom. One MRI system geometry depicted in FIG. 1 includes asubstantially coaxial cylindrical arrangement of the static field B0magnet 12, a G_(x), G_(y) and G_(z) gradient coil set 14 and an RF coilassembly 16. Along the horizontal axis of this cylindrical array ofelements is an imaging volume 18 shown as substantially encompassing thehead of a patient 9 supported by a patient table 11.

An MRI system controller 22 has input/output ports connected to display24, keyboard 26 and printer 28. As will be appreciated, the display 24may be of the touch-screen variety so that it provides control inputs aswell.

The MRI system controller 22 interfaces with MRI sequence controller 30which, in turn, controls the G_(x), G_(y) and G_(z) gradient coildrivers 32, as well as the RF transmitter 34 and the transmit/receiveswitch 36 (if the same RF coil is used for both transmission andreception). The MRI sequence controller 30 includes suitable programcode structure 38 for implementing a spatial-modulation pre-sequence(e.g., SPAMM or DANTE) in conjunction with other (e.g., conventional)MRI sequences already available in the repertoire of the MRI sequencecontroller 30.

The MRI system 20 includes an RF receiver 40 providing input to dataprocessor 42 so as to create processed image data to display 24. The MRIdata processor 42 is also configured for access to a B1 and/or B0 mapprogram code structure 44 and to a B1 and/or B0 map memory 46 (e.g., forstoring B1 and/or B0 map data derived from processing in accordance withthe exemplary embodiments and the B1 and/or B0 map program codestructure 44).

Also illustrated in FIG. 1 is a generalized depiction of an MRI systemprogram store 50 where stored program code structures (e.g., for B1and/or B0 mapping based on spatial frequency domain analysis) are storedin computer-readable storage media accessible to the various dataprocessing components of the MRI system. As those in the art willappreciate, the program store 50 may be segmented and directlyconnected, at least in part, to different ones of the system 20processing computers having most immediate need for such stored programcode structures in their normal operation (i.e., rather than beingcommonly stored and connected directly to the MRI system controller 22).

Indeed, as those in the art will appreciate, the FIG. 1 depiction is avery high level simplified diagram of a typical MRI system with somemodifications so as to practice exemplary embodiments to be describedhereinbelow. The system components can be divided into different logicalcollections of “boxes” and typically comprise numerous digital signalprocessors (DSP), microprocessors, special purpose processing circuits(e.g., for fast A/D conversions, fast Fourier transforming, arrayprocessing, etc.). Each of those processors is typically a clocked“state machine” wherein the physical data processing circuits progressfrom one physical state to another upon the occurrence of each clockcycle (or predetermined number of clock cycles).

Not only does the physical state of processing circuits (e.g., CPUs,registers, buffers, arithmetic units, etc.) progressively change fromone clock cycle to another during the course of operation, the physicalstate of associated data storage media (e.g., bit storage sites inmagnetic storage media) is transformed from one state to another duringoperation of such a system. For example, at the conclusion of a B1and/or B0 mapping process, an array of computer-readable accessible datavalue storage sites in physical storage media will be transformed fromsome prior state (e.g., all uniform “zero” values or all “one” values)to a new state wherein the physical states at the physical sites of suchan array vary between minimum and maximum values to represent real worldphysical events and conditions (e.g., the sensitivity map for an RFantenna/coil over an imaging volume space). As those in the art willappreciate, such arrays of stored data values represent and alsoconstitute a physical structure—as does a particular structure ofcomputer control program codes which, when sequentially loaded intoinstruction registers and executed by one or more CPUs of the MRI system20, cause a particular sequence of operational states to occur and betransitioned through within the MRI system.

The exemplary embodiments described below are superior ways to processacquisitions and compute B1 and/or B0 maps from images which haveintensity modulation from tagging pulses.

The acquired single image has a spatial modulation imposed on it. Thebasic spatial frequency of the modulation is known, to within lesservariations which arise from B0. The amplitude of the modulation dependsupon the strength of RF pulses and hence the spatial B1 (transmit field)dependency. Raw MR data (k-space data) for these scans includes acentral section which generates the unmodulated (i.e., low-frequencybase band) part of the image.

In a preferred embodiment, the k-space data is reconstructed to an imagein the spatial domain in the usual way, including an (inverse) 2DFT andtaking the magnitude of the complex image. A further (forward) 2DFT isthen used to convert it back to the k-space spatial frequency domainwhich contains shifted replicas which generate the higher frequencymodulated components of the image. Simple windowing operations separatethe modulated and unmodulated components (in k-space). The k-space dataincludes a “low-pass” unmodulated part of the signal, a “high-pass”modulated part with a positive spatial frequency, and a “high-pass”modulated part with a negative spatial frequency. Each of the parts (thetwo modulated parts and the unmodulated part) are then independentlytransformed back to the image domain. Taking the magnitude (in the imagedomain) of complex quantities demodulates the modulated parts. One mightchoose to call these contributions “modulated-unmodulated” parts. Sumsand differences of those parts, in turn, give robust maps of the maximalsignal envelope and minimal signal envelope. The unmodulated part plusthe modulated-unmodulated parts gives the peak envelope. The unmodulatedpart, minus the modulated-unmodulated parts gives the trough envelope.These generated envelopes are more accurate than quantifying peaks andvalleys in the image domain. The technique is fast enough to beacceptable for calibrations or pre-scans, if needed, in clinicalscanning applications.

The filtering in k-space can be done by multiplying the data by, forexample, two, three (or more) window functions. A first window, for thelow-pass, can be positioned over the center of k-space, i.e., the D.C.component. Alternately, it is feasible to search the k-space data todetect the location with the highest peak, and to use that as the centerfor the low-pass window.

The locations at which to apply the at least one high-pass window (e.g.,two in this exemplary embodiment, one for positive and one for negativespatial frequencies, respectively) can be determined in any of a fewways. The area of the gradient pulse used between the two RF taggingpulses can be multiplied by a Larmor frequency, to give a k-spacedistance, in units such as cycles per centimeter. This distance, plusknowledge of the imaging field of view, can be used to determine adistance in terms of a number of samples (presuming for example,critical Nyquist sampling rates). As an example, if the gradient arearesulted in a cycle of accumulated phase every 6 millimeters, and if theimaging field-of-view were 24 centimeters, then the modulation amountsto 40 cycles of modulation across the image. Thus, by the Fourier shiftprinciple, the modulated parts will be displaced by 40 samples to eitherside of the unmodulated low-pass central data. Therefore, one maymultiply one copy of the k-space data by a window shifted 40 indices toone direction, and multiply another copy of the k-space data by anidentical window shape, but displaced 40 indices in the oppositedirection from the center. The particular window functions could be anyof a wide set of shapes, such as Hanning, Hamming, Gaussian,Kaiser-Blackman, Fermi functions, etc., as are well known in signalprocessing and in MRI. An alternative to calculating the shift fromgradient and sequence parameters is to search the k-space data to detectthe location of these secondary peaks.

The windowing operations in k-space provide a kind of filtering andreduce noise, allowing better determination of peak and trough signal.But a more significant advantage arises from the fact that theunmodulated-modulated image-domain data and the low-pass unmodulateddata now have their minor oscillations removed, and have meaningfulvalues at all pixels. Areas with no signal will have values near zero.Thus, it is possible to form a ratio of two components at the samepixel. At a pixel which previously would have been a trough, there isnow what amounts to an interpolated or fitted value which gives areasonable estimated value of a peak at the same location. At a pixelwhich previously would have only been a peak, there is likewise anavailable estimate of a trough. And in between, there are high-qualityfits to both peaks and troughs. Thus, the main source of error isremoved, which used to arrive from changes in tissue signal as one movedfrom a peak location to a trough location. This greatly improves thequality of the B1 map in areas where the MRI tissue characteristicschange.

On a pixel-by-pixel basis, the next step is to form a ratio of theminimal signal to the maximal signal. This ratio can be called the “tagdepth” where a value approaching zero indicates near complete darkening(saturation) by the total tagging RF angle. The total tagging RF angleis then determined by taking the inverse cosine (arc cos) or cos⁻¹ ofthe tag depth TD=min/max. When the min is close to the max, TD is justless than one, and the tagging has minimal effect. When min is close tozero, then TD is also small which indicates the efficacy of the imposedtagging is close to 100% saturation.

Optionally, alternative measures might be generated for storage ordisplay. For example, a “tagging efficiency” defined as (1-min/max)might be favorable for ease of human comprehension, as a value near 1.0would then represent highly effective tagging saturation and 0.0 wouldbe completely ineffective tagging.

The B1 field can be saved in any of a few representations. It isreasonable to express the value at each pixel as the magnetic fieldstrength of the effective transmit RF field. Alternately, it isreasonable to show the flip angle of a particular pulse, or the totaltagging RF pulse.

Another favorable representation of the B1 map is to form a ratio,giving the actual local value normalized by the nominal value specifiedin the sequence. This ratio could be formed between tip angles, orbetween B1 field strengths, etc. In such a representation, a value over1.0 would indicate “over-tipping”; 1.0 is the ideal value, and valuesunder 1.0 indicate under-tipping. Such a representation can be usefulbecause it includes not just the spatial variation of the B1 Tx field,but it also captures any effects of calibration or system gain errors.It characterizes the entire MR system transmit RF, including possibledeviations in calibration, transmitter gain, etc.

Within reason, the time from the tagging to the excitation pulse shouldbe kept short, especially compared to the T1 values of the materials, tominimize a source of bias, where T1 relaxation of the tagged nucleicould cause their amplitude to be under-estimated, and the B1 value alsounderestimated. Similarly, the duration of each individual tagging pulseshould be kept short, as otherwise off-resonance during a pulse can leadto different effective tip angles. In particular, off-resonance canintroduce a bias, and underestimating of the RF pulse angle and the B1.

A typical data acquisition sequence is depicted at FIG. 2 where a SPAMMpre-sequence precedes a conventional MR imaging sequence. Here, in thisparticular example, two 30° RF nutation pulses are transmitted into theimaging volume and between them, a SPAMM magnetic gradient pulse isinterleaved. The spatial modulating frequency will be proportional tothe integral of the tagging gradient. An optional spoiler pulse may alsobe employed after the pre-sequence and before the conventional MRimaging sequence begins. As will be appreciated, the received RF signalsoccur later during the conventional MR imaging sequence. However, theywill have been spatially modulated because of the pre-sequence depictedat FIG. 2. In the example of FIG. 2, the SPAMM spatial encoding (i.e.,“tagging”) gradient pulse is imposed by using G_(y) (typically the phaseencoding gradient in a conventional MR imaging sequence), although itcould also be imposed via the G_(x) gradient (which is shown inparenthesis in FIG. 2). The optional spoiler pulse could be provided byany of G_(x), G_(y) or G_(z). Typically, G_(z) is used as the“slice-select” gradient during subsequent RF excitation pulses in aconventional MR imaging sequence, while G_(x) is applied during read-outof, for example, an RF echo response in the time domain so as tofrequency encode the read-out RF signals in the x spatial dimension.

A high level schematic depiction of an exemplary process is provided atFIG. 3. Here, at 300, k-space MR image data is acquired with cosine-likespatial modulation (e.g., at a spatial frequency k_(f) that isdetermined by the tagging gradient used during the pre-sequence as notedabove).

As earlier indicated, some advantages can be had by twicetwo-dimensionally Fourier transforming the originally acquired k-spacedata so as to create a processed “starting” k-space data set beforefrequency filtering operations are performed in accordance with thisembodiment.

As depicted on the right side of FIG. 3 at 301, one row of k-spaced datain the spatial domain will have superimposed modulation at a spatialfrequency k_(f).

The “starting” k-space data set is then frequency filtered at 310, 320and converted to the spatial domain (e.g., by 2DFT). The filter bank 310is a low-pass filter providing magnitude output L, while the filter bank320 is a high-passband filter with passbands located above and below thelow-pass filter bank at +−k_(f). (The high-pass filter could alternatelybe a bandpass filter, with a passband centered near the nominal SPAMMspatial modulation frequency. In subsequent references to “high-pass”,it is recognized that either high-pass or bandpass implementations canbe used, and the intent is to include both cases.) The filtered higherpassband spatial domain data sets (e.g., based on harmonics of the baseband signal) are then demodulated at 330 (e.g., by taking absolutevalues of complex values) to provide a pair of higher frequencyenvelopes +E and −E. Rough schematic depictions of an exemplary one rowof data across the image in the spatial domain are depicted to the rightin FIG. 3 for each of these outputs.

At 340, a smoothed “upper” curve (L+E) is derived, while at 350, asmoothed “lower” curve (L−E) is derived. Once again, a depiction of onerow of data across the image in the spatial domain is shown to the rightside of FIG. 3.

At 360, a “tagging depth” ratio R can be calculated at each pixel bytaking a ratio between the “lower” and “upper” data magnitude values.This ratio can then be converted at 370 to an effective nutation RFpulse angle θ (which is proportional to B1 magnetic field strength) byusing an inverse trigonometric function. For example, the quantity L/Ucan be used in conjunction with the arccos function so as to compute θ.Of course, as will be appreciated, θ can be converted to B1 magneticfield strength and either or both θ, B1 values can be normalized withrespect to the nominal expected control values used for the originalpre-pulse nutation modulation.

Finally, at 380, the resulting θ, B1 map data can be displayed, storedin machine-readable accessible storage media, or otherwise used (e.g.,by retrieving it from storage data) to compensate a diagnosticimage—perhaps for the very same patient anatomy that was in place duringthe derivation of the B1 map data.

A more detailed program code structure is depicted at FIG. 4 for the MRIsystem of FIG. 1. Here, if a B1 mapping process is chosen, the processis initiated at 400. Thereafter, at least one set of k-space data taggedwith spatial modulation is acquired at 402. For example, it may beacquired with a known spatial modulation frequency f_(m). Althoughvarious sizes of k-space data arrays may be used (e.g., 32×32, 64×64,128×128, etc.), for a hypothetical example, it may be assumed that f_(m)is equal to one cycle every 2 cm or 0.5 cm⁻¹. Let it also be assumedthat the k-space array is a 128×128 point array covering a square 256 mmslice of the imaging volume. This equates to an approximately 0.2 cm perpixel resolution, meaning that there are about five line-pairs ofspatial modulation per centimeter, and a total distance of about 12.8k-space data points between harmonics of the base band signal appearingat the origin of k-space (i.e., k_(x)=0 and k_(y)=0 at the center ofk-space). In this example, then a base band strip of k-spaceapproximately twelve lines wide and centered upon the middle “zero” linewould constitute the baseline low frequency filtered portion of k-space.A similarly sized strip just above the baseline strip of about twelvelines wide would then constitute the high-pass “positive” filteredsegment of k-space, while a similar twelve line segment or strip locatedjust below the baseline across k-space would constitute the high-pass“negative” frequency filter passband.

As those in the art will appreciate, the variables could otherwise bechosen such that the entirety of k-space would simply be divided intothirds with the middle third being the base band low-pass frequencycomponent and the upper and lower thirds being the positive and negativehigh-pass filtered components, respectively. When k-space is evenlydivided in this manner, it facilitates the design of the transitionbands of the high-pass and low-pass filters, as will be appreciated bythose in the art.

If desired, at 404, a decision point may be inserted as to whether ornot one wishes to compensate for MRI system variables by performing afirst two-dimensional Fourier transform of the original k-space data at406 into the spatial domain and then a second two-dimensional Fouriertransforming from the spatial domain back to the frequency domain at 408before arriving at a suitable “starting” k-space data set. Of course, asthose in the art will appreciate, this may be done automatically all thetime or never rather than to provide a user-controlled decision point404.

The appropriate desired “starting” k-space data is then frequencyfiltered by dividing it into at least three portions (in this exemplaryembodiment): a low-pass baseline part=LP, a high-pass positive modulatedpart=HP+ and a high-pass negative modulated part=HP−.

Each of the frequency filters (e.g., extracted parts) of k-space dataare then two-dimensionally Fourier transformed so as to convert themback to the spatial domain—and demodulated by using only the magnitudeof the spatial domain values at 412, 414 and 416, respectively.

Thereafter, on a pixel-by-pixel basis, all three of the filteredsub-sets are summed at 418 to provide a map of peak or maximum signalenvelope values. At 420, a difference is taken between the low-passbaseline magnitude values and the sum of the high-pass side bands so asto provide a pixel-by-pixel map of the trough or minimum signal envelopevalues.

Thereafter, at 422, on a pixel-by-pixel basis, a tagged depth value iscalculated which, in this exemplary embodiment designed for useultimately with an arccos function, is calculated at min/max. As will beappreciated, at each pixel, this value then involves taking the ratio ofthe minimum to maximum values.

Thereafter, in this exemplary embodiment, at 424, the arccos of thetagged depth value is calculated for each pixel so as to derive aneffective RF flip pulse angle θ for each pixel, thus providing a map offlip angle θ values. If desired, the θ values may be converted to B1magnetic field strength values at 426 using well known formulae.

In addition, if desired, normalized θ and/or B1 map values can begenerated at 428. Any or all of such θ, B1 map values are then storedand/or displayed and/or printed at 430 as may be desired. Such mapvalues can also be used at 432 so as to compensate diagnostic imagesfrom the MRI system (perhaps from the very same patient that was used togenerate the B1 maps) and/or to design improvements to the MRI systemand the like, as will be appreciated by those in the art. Exit from thisroutine is taken at 434 and, as schematically depicted in FIG. 4, theprogram code structure may be configured with optional exits (or jumpsto a desired type of mapping) at many desired points (e.g., at 436, 438,440, 442 or 444).

Some enhancements (enumerated as 1-15E below) can provide optimizationsof the acquisition pulse sequence, as ways to enhance the overallperformance of B1 mapping. In narrow terms, the exemplary embodiment ismainly a processing and analysis process. But in broader terms, theoverall method can be improved in some cases, by coupling the processingwith an enhanced acquisition, and that acquisition enhancement may nothave special significance outside its use with the exemplary embodimentsdesired herein.

Enhancement 1: Higher harmonic terms may be used to fit more complicatedmodulations. This can extend the dynamic range of RF tagging pulseamplitudes, beyond the sinusoidal patterns associated with magnitudeimage reconstruction and tags of less than 90° RF amplitude. Differenttag line patterns are shown in the Bernstein, King and Zhou book. Forexample, to extend dynamic range of tagging pulses, one couldcharacterize the tagging shape, by showing how the first two, three orfour Fourier components of the modulation pattern are expected to varywith the total tag RF angle. Then, one can window and reconstructmultiple harmonics independently, and finally one can select the taggingangle which has the expected ratio of components which most closelymatch the data at a pixel.

Enhancement 2: The time shift between the component RF pulses insideSPAMM-like tagging pre-pulse can be constrained, so that the shift ofthe tag lines for the off-resonance difference between fat and water issubstantially a multiple of the time period needed for one cycle ofphase to accrue between these species. For example, at 3 T, the taggingpre-pulse could be generated by two pulses, timed such that the delayfrom the center of one pulse to the center of the next pulse is about2.3 milliseconds. This time increment is known in other MRI pulsesequences as a “fat-water in-phase echo time”. The reason to do such isso that the location of stripes in fat and stripes in water signal arethe same, and fractional shifts of the RF tagging pattern are notencountered when crossing a fat-water interface. This makes thefiltering and separation of the modulated component more robust.

Enhancement 3: If an echo train-based readout technique [EPI, FSE, FASE]is applied after the tagging, the effects of amplitude decay modulationof the echo train must be considered. The effect of the amplitude decayshould be identical in each replicant. Otherwise, if different signalcomponents were centered at different parts of the amplitude decay, thenthe different replicants would have different T2 decay, and theiramplitudes could not be directly used in ratios, without error orbiases. Therefore, the shift direction of the replicants should occuralong the readout direction in k-space.

Enhancement 4: The filtering of the k-space data as described is alongone direction. The resultant B1 map will have its spatial resolutionlimited in that direction. However, in the opposite direction within theimage, higher spatial resolution may be obtained. Filtering can involvecollecting and merging in two directions—one of which achieves goodresolution near a horizontal edge direction, and the other of whichachieves good resolution near a vertical edge direction.

Enhancement 5: If two excitations are desired without waiting for fullrecovery, this might be done by collecting them with different spacingtag orientation shifted 90° (or tag spacing shifted). While the firstset of tags may not have fully recovered, that first set can be ignoredif it falls outside the window (in k-space) which would be needed tofilter and separate a second set of tags, and so on.

Enhancement 6A: Signed or complex image input may be utilized (i.e., notthe usual magnitude reconstruction of complex signal). Then, themodulation range can exceed a 90° total tagging angle, for betterdynamic range, while still using simple k-space filtering of the firstsinusoidal harmonic in the tagging pattern.

Enhancement 6B: When the spatial domain images used are magnitude orreal, as opposed to complex, then it is noted that the k-space datacontains Hermitian symmetry. It is possible to take direct advantage ofthe fact that shift frequency bands at positive and negative frequenciesare related by reflection about the center of k-space, and by complexconjugation. Thus, it is possible to perform alternate equivalentoperations such as windowing only the positive shifted frequency band,performing a 2DFT on it, and then generate the equivalent shiftedfrequency results by taking the real part of the 2DFT result andmultiplying it by 2. These variations derive from the basic mathematicalproperties of the Fourier transform, and are well known in the art.

Enhancement 6C: When the images used are complex, it is also possible towork with just one of the shifted frequency sidebands instead of boththe positive and negative direction shifted frequencies. As one example,it is possible to use one sideband, either the positive frequencyharmonic or the negative frequency harmonic, double its contribution,and not use the other shifted frequency sideband at all, while acceptingsome artifact or degradation in the resultant 2DFT spatial domainresults. It is also possible to use known MRI reconstruction techniquesfor reconstruction of partial datasets, in a way which reduces theartifacts. For example, a low resolution phase map can be generated fromthe main low-pass frequency image, and this phase map can be used forcorrection when synthesizing an equivalent 2DFT spatial domain imagecorresponding to what would result from the negative sideband. Thesekinds of methods are well known in the MR literature, where they arecommonly known as partial Fourier reconstructions, asymmetric k-spaceacquisitions, conjugate symmetry reconstructions, and the like.

Enhancement 7: At a major edge, such as the exterior of the body, therecan be point-spread issues which differ between the high-pass andlow-pass portions. This can lead to bad computed data for the flip angleor B1 in those areas. Similarly, this can occur near signal voids. Onestep in the processing can be to generate a mask to identify areas ofvery low signal, or very significant signal gradients, or both. Then anerosion operator may be used on the mask image, to remove edge regionsin the B1 map, which may have larger error.

Enhancement 8: Besides the map of B1, a secondary map such as ρ can begenerated, or a mask can be formed by thresholding of ρ, so that insubsequent operations using the B1 map, it is known for which pixels wehave generated a reasonable estimate of B1, and for which pixels thereis no such estimate available.

Enhancement 9: Relative amplitudes and/or relative phase of distinct RFtransmit channels could be determined by an extension of this method.Consider a system with two transmit coils. The acquisition pulsesequence could be repeated two or three times. In a first repetition, asingle transmit coil or channel could be used for both of the RF taggingpulses. In a second repetition, the two RF tagging pulses can be appliedwhere one coil is used to transmit the first pulse of the tagging pair,and the second coil is used to transmit the second RF pulse of thetagging pair, in which phase-sensitive maps of the modulation(high-pass) components can be generated from each map.

Optionally, a third repetition can be performed in which the second coilis used for both pulses. From the basic phase difference of the twomaps, one can compute the relative phase difference of the two transmitcoils. Many different similar alternatives should be easy to conceive byone skilled in the art, such as extension to larger numbers of coils.

Enhancement 10: Tagging structures other than two-pulse SPAMM can beused (however, the sinusoidal modulation that arises from two-pulseSPAMM does correspond to a particularly easy case for filtering ink-space, and for demodulating). In particular, any pattern that hasstructure which is locally substantially periodic should be a candidatefor filtering and separation in k-space.

Enhancement 11: The example diagram herein for processing shows theprocess beginning with magnitude images, then optionally performing areverse transform to convert back to a k-space data representation. Thiscan have certain practical advantages, such as implicitly allowing foruse of auxiliary functions that are performed in a productreconstruction (combination of data from multiple receiver coils beingone example). However, it is not necessary to convert to and from theimage domain before filtering. An alternative is to directly applywindow filtering and separation to the raw acquired k-space data,without first performing forward and backward transforms.

Enhancement 12A: Single-shot acquisition is a suitable choice for theimaging readout of this method (for example, single-shot EPI, orsingle-shot FSE, or as is available in Toshiba® MR application software,single-shot FASE). It is also reasonable, however, to use amultiple-shot imaging readout. If a multiple shot readout is used, thenthe preferred implementation is to allow the signal to recover from thetagging pulses, before re-applying the tag and collecting the next shot.For example, the recovery time could be in the range of three to fourtime constants of the typical range of T1 encountered in the tissues.This general advice would apply to any tagging analysis, and may not bespecific to the k-space filtered analysis.

Enhancement 12B: If more than one shot is needed, or more than oneimage, then one can contemplate using a saturation and spoiling pulsedirectly after each imaging readout. This would enable faster readout,i.e., maybe somewhat faster than TR=T1, without leaving residual bias tothe tag line intensities (the bias arising from unequal saturation andincomplete recovery). This general advice would apply to any tagginganalysis, and may not be specific to the k-space filtered analysis.

Enhancement 13: When extending the technique from 2-D maps, to 3-D maps,3DFT is a good choice if SNR is more limiting than motion. Alternately,sequential 2DFT acquisitions, separated by significant time for the tagsto recover between each slice, is a good choice of an imaging readoutsequence whenever control of patient motion is more critical than SNR.This general advice would apply to any tagging analysis, and may not bespecific to the k-space filtered analysis.

Enhancement 14: If windowing of the central lobe and shifted replicantsis done in one dimension, then signal energy from distant areas ofk-space may appear in the wrong window. This may lead to artifacts, suchas diagonal edges in the B1 map exhibiting a stair-stepping pattern orlocal superimposed “zebra stripes”. One simple way to reduce therelative error from signal being included in the wrong window is toapply a filter or window along the opposite direction in k-space. Theresult is a 2-D window or filter as depicted in FIG. 5.

Near the center of one replicant echo, for example, the power of thesignal from the modulated signal part will greatly exceed the power ofthe other two parts (unmodulated part, and other replicated part withwhose frequencies have the opposite sign). But at farther distances ink-space, the error signal from the other parts becomes comparable to, orpossibly even greater than, the power from the correct modulated part.Thus, these more distant areas contribute relatively more error, andshould have reduced weighting or should be completely windowed out ofthe individual processing of the individual components.

Another method to reduce error is simply to acquire fewer lines ofk-space.

As depicted in FIG. 5, the main unmodulated base band signal 500 appearsshifted to the left for a first “negative” harmonic at 502, and shiftedequally to the right at 504 for the first harmonic modulated “positive”signal in k-space. The diagonally extending hash marks from each of theprinciple lobes (depicted by circled crosses or plus signs) can thus beseen to extend into the center window region at 506 from the upper andlower side bands or harmonics. Accordingly, to help diminish thisunwanted effect, a 2-D window rather than complete strip of k-space canbe employed at 508 so as to filter out at least some of the interferingripples from adjacent side bands/harmonics. Similar 2-D windows (e.g.,rectangular, square, circular, etc.) can be utilized for all threecomponents of frequency filtering in k-space as depicted at 510 in FIG.5.

Enhancement 15A: The distant k-space signal from one signal component(i.e., from the unmodulated-component, or from themodulated-positive-frequency-component, or from themodulated-negative-frequency-component) can appear inside the mainfiltering window of another component (as also mentioned in enhancementor alternate embodiment 14). This signal can be thought of as a kind ofbaseline ripple, upon which the correct signal component is added. Ifthe baseline ripple can be reduced or removed, then the artifact will bereduced or removed. We now describe four technical ways to reduce orremove the “baseline” ripple.

Enhancement 15B: As depicted in FIG. 6, one can collect one taggedacquisition with the tags oriented in one direction (e.g., as in 602with the tagging gradient along the X direction for a transverselyoriented B1 map), and also collect a second tagged image, with the tagsoriented along the opposite in-plane direction as in 604, that is alongthe Y direction. With the two acquisitions in the two directions,replicants will occur with data at four locations, i.e., +kx, −kx, +kyand −ky. Select the scan parameters, including, for example, the k-spaceecho order and the phase encoding direction, so that as much as possiblewithin reason, the echo decay at the same locations in k-space is thesame. When the tagged components are shifted along the (plus-or-minus)kX direction, save a copy of the baseline ripple as detected by thewindows situated at the (plus or minus) ky-shifted locations at depictedat 606. When, in the other acquisition, the tagged components areshifted along the (plus-or-minus) kY direction, save a copy of thebaseline ripple as detected by the windows situated at the (plus orminus) kx-shifted locations. Subtract a copy of the measured baselineripple in each shifted window from the acquired modulated signal in thatsame window as shown at 610, 612, to at least partially reduce thebaseline ripple. Combine the maps from the two corrected acquisitions.

If the sequence uses an echo train-based readout technique (EPI, FSE,FASE, etc.), multiple shots of segmented k-space should be used. Here,the choice of phase encode schedule per shot is important. The phaseencode schedule dictates the amplitude decay modulation function. In thefirst acquisition (tag along X), by acquiring the readout directionalong the same direction of the shift (+/−kx), the central low frequencycomponent and outer high frequency components are centered within thesame position of the amplitude decay modulation function. All componentsexperience the same amplitude decay modulation. In the secondacquisition (tag along Y), the phase encode direction must be the sameas the first acquisition. Only the direction of the shift should change(to +/−ky). The components must all be centered in the same positions ofthe phase encode schedule within each segment. The segment size, phaseencode schedule and/or tag cycle spacing must be chosen accordingly.Therefore, for the technique of baseline removal, if using an echo trainreadout method, the number of shots (segments) might naturally be amultiple of 3. A separate shot can be used for each component in thesecond acquisition to ensure that the component is centered in theamplitude decay function the same way. In this way, the ripple estimateregions of interest (A, B, C, D in FIG. 6) and the shifted componentsare all affected by the same amplitude decay modulation function in thesame way. Since the ripple estimate regions have the same amplitudedecay modulation as their corresponding shifted components, a directsubtraction can be performed.

Enhancement 15C: As in 15A, collect data with two (or more) orientationsof the tag data. Generate an uncorrected B1 map from each acquisition.Combine the images on a pixel-by pixel basis, such as by simpleaveraging, or by performing a weighted combination, with preferentialweighting at each location in image space for the B1 map which has theleast high-frequency content potentially interfering with the taggingmodulation patterns of each tagging orientation.

Enhancement 15D: Collect one copy of the acquisition with tags, and onewithout tags. Note the location where filter windows are placed over theshifted signal components with modulated signal in k-space. Fromcorresponding locations of windows over the untagged scanned k-spacedata, extract copies of the high frequency k-space data (these would bethe baseline ripples). Optionally, determine an amplitude factor,showing how the central untagged component of the data has reducedoverall amplitude in the k-space. Subtract the baseline ripple estimates(optionally multiplied by the factor for reduced amplitude). Proceedwith the rest of the map generation process.

Enhancement 15E: Collect two acquisitions, each of which could be usedto generate a B1 map. The first acquisition pre-pulse sequence shown inFIG. 7 a is as previously described for FIG. 2. However, in the secondacquisition at FIG. 7 b, the sequence is modified so that the spatiallocations of the peaks and troughs in the (sinusoidal) tagging patternare reversed. This may be done by inverting the polarity or phase of oneof the two RF tagging pulses. Suppose the first acquisition has atagging sequence which is symbolically denoted as (+αRF, Gtag_encode,+αRF). Then the second acquisition can have a sequence which issymbolically denoted as (+αRF, Gtag_encode, −αRF).

Extract the three components from each of the two acquisitions (asshown, respectively, at FIGS. 7 c and 7 d in which these six componentsare labelled as LP+alpha, LP−alpha, HP+alpha+freq, HP−alpha+freq,HP+alpha−freq, HP−alpha−freq where the part of the label either “+alpha”or “−alpha” refers to which RF polarity is used in the two acquisitions.Then, form some combinations by additions and subtractions:LP=(LP+alpha)+(LP−alpha)HP+freq=(HP+alpha+freq)−(HP−alpha+freq)HP−freq=(HP+alpha−freq)−(HP−alpha−freq)

where LP is the low-pass (or unmodulated) component, and HP+freq andHP−freq are components which are modulated (high-pass) and shifted topositive and negative frequency displacements.

This phase cycling scheme causes cancellation of the baseline ripple.Other variants of phases will be obvious to those skilled in the art,i.e., they are corrected so as to have the contribution from theunwanted signal removed.

Proceed with the rest of the map generation process.

FIGS. 8, 9 and 10 are photographs of a particular implementation ofalternative 15E. Here, FIG. 8 shows the spatial domain image of a pelviswith the tagging lines shown. FIG. 9 is a normalized nutation angle θmap generated from the tagged image of FIG. 8. FIG. 10 shows the θ mapof FIG. 9 with superimposed contour lines where 1.0 means measured totaltip angle matches what was nominally specified, 0.80 means that the tipangles are 20% below that which was nominally specified, etc.

SPAMM tagging by the use of binomial 1-1 pulses makes for easycomputation, ignoring relaxation effects. In the under-tipped saturationcase, local minima and maxima are detected in similar tissue, making iteasy to solve for RF tip angles at each pixel:

$R = \left( \frac{saturatedSignalMin}{unsaturatedSignalMax} \right)$tipAngle = 0.5 × arccos (R)

where:

tipAngle=angle of one (square) RF pulse in the tagging pre-pulse. Thenthe net saturation effect of pair of RF pulses in the single pre-pulsevaries spatially from 2*tipAngle down to zero.

An alternate form of equation for calculating the tipAngle is based onfractionOfSaturation FS=1−R where tipAngle=0.5 arc sin (FS). Yet moreforms of inverse trigonometric relationships can be listed, acting uponother simple functions of the various images, but they are allmathematically equivalent.

As shown in FIG. 11 a, an untagged image will provide pixel values alonga line therethrough. Inside the magnet and the subject, the RF coilsgenerate a transmit field, which has a spatial distribution asrepresented in FIG. 11 b. The two tag RF pulses in the SPAMM pre-pulseare capable of generating a tagging strength, with a fraction ofsaturation “f_sat” as illustrated in FIG. 11 c. The tagging gradientinside the SPAMM pre-pulse, however, causes an actual tag spatialprofile with a nominally sinusoidal profile, as illustrated in FIG. 11d. The intensity of spins immediately in the SPAMM image is then shownin FIG. 11 e, where the tagged image is the multiplicative product ofthe untagged image and the tag spatial profile. An intermediate goal forsome of the processing steps within the entire B1 tagging k-space methoddescribed herein is to recover good estimates of upper and lowerenvelopes.

Estimating the envelopes can yield intermediate useful results asillustrated by the bold lines in FIGS. 12 a and 12 b, but these willreally be 2-D images/surfaces, not just 1-D curves as depicted.

Here:PeakEnvelope=Lowpass+Bandpass_DemodulatedValleyEnvelope=Lowpass−Bandpass_DemodulatedFractionOfSaturation=1−(ValleyEnvelope/PeakEnvelope)where the depicted bandpass and low-pass are effected in k-space, thedemodulation is effected in image space (by taking magnitude). Thebandpass data might be termed either “bandpass” or “high-pass” data.

As depicted in FIGS. 13 a-13 c, partial amplitude modulation producestwo shifted “replicants” in k-space. Here, FIG. 13 a depicts how k-spacelooks for the untagged image. FIG. 13 b shows a simple tag spatialprofile. Applying the tag spatial profile onto the untagged image oruntagged k-space results in the reduction of the central lobe, plus thegeneration of the left and right lobe (shifted) replicants. Amplitudesof the shifted replicants depend on:f=FractionOfSaturation/2 (e.g., assume: 0.0<=f<=0.5).

FIG. 14 illustrates an exemplary program code structure for dataacquisition, filtering and processing of k-space data to produce a B1field map. This is an alternate representation of the k-space tagprocessing, similar to that described in relation to FIG. 3 or 4.

However, there is a difference between using sines and cosines, in imagespace or in k-space. Suppose an image exhibits cosine-like behavior(symmetric about the center). Then all of the k-space signal is real andsymmetric. But if the image exhibits sine-like behavior (anti-symmetricabout the center), then all of the k-space signal is imaginary andanti-symmetric.

Recall that sines and cosines with arbitrary initial phase angles can bewritten as a sum of sines and cosines with zero initial phase angles.This is basic trigonometry, and also very well known in complexvariables, and very well known in dealing with Fourier transforms.

The basic result is that the sine-like component of the modulatedwaveform will show up as anti-symmetric and imaginary parts in thek-space replicants and the cosine-like components will be real andsymmetric in the two k-space components. Therefore, the relative amountsof real and imaginary portions of the k-space replicants are directlyrelated to the relative amounts of sine-like and cosine-like componentsin the “bandpass” image data.

The physical meaning of “initial phase” in the tagging grid can also beconsidered. Suppose signal is perfectly on-resonance, and suppose twosquare SPAMM RF pulses are of the same polarity. Then, at gradientisocenter, those pulses will act in unison and the net effect is maximalsaturation. The net effect is a “valley” at isocenter where the signalin the bandpassed (high-passed) image is real and negative (beforetaking the magnitude).

If instead there is accumulated phase of 180 degrees (due to gradients,or off-resonance, etc.), then the net effect is zero saturation atisocenter and a peak of the tagged image will occur at isocenter. Thesignal in the bandpassed (high-passed) image is real and positive (atisocenter) (before taking the magnitude of the complex quantity.)

In either of these cases, the two replicants in k-space are symmetriccompared to each other.

If instead 90 or −90 or 270 or −270, etc. degrees of phase accumulatesfrom the first alpha pulse to the second alpha pulse, then one is atmiddle amplitude, which is exactly what is fully captured in the“low-passed” central replicant. The two left and right lobe replicantsin k-space are anti-symmetric compared to each other.

Tag lines can be locally misplaced or “bent” where off-resonance is moresignificant. For example, generally near air or body cavities,susceptibility may cause off-resonance.

Suppose the majority of the image is essentially on-resonance (i.e., amajority of the B1 and B0 fields are uniform). But in areas where thesignal is off-resonance, the tagging grid will now be locally shifted.This distortion can be thought of in at least three related ways: (1)The image-domain lines can be seen as bent or displaced. (2) Sinusoidalpatterns convert to cosine patterns (i.e., anti-symmetric and symmetricwith respect to some center) and vice versa. (3) The complex phase ofvarious signals is converted from real to imaginary and vice versa(which can be seen either in the image domain or the k-space domain, ifthe signal has not been converted to magnitude in that domain).

Now it is also possible to convert a signal's complex phase into anamount of off-resonance, i.e., a B0 map. A simple way to do so uses mostof the same processing steps as already explained for B1 processing.Program code for effecting B0 map processing of windowed replicants ink-space is depicted graphically in detail at FIG. 15.

FIGS. 16, 17 and 18 show exemplary B1 and B0 maps produced by theabove-described processes. Some practical details associated with thegeneration of these exemplary images include: use the existingconventional magnitude image reconstruction of the scanner, employnecessary support for partial Fourier transforms, array coilcombination, etc., then back-transform to idealized k-space.

Typical readout pulse sequence parameters are FSE2D, partial Fouriertransform, TE 39, TR 2250, EchoSpacing 6.5 msec, 54 echo train length, 2shots per image, 2 tag polarities, 4 imaging shots, total acquisitiontime is 12-14 seconds including FSE calibration pre-scan, readoutresolution 192×256 samples, and B1 map resolution up to 192×85 (since 85approximately equals 256/3 windows).

When this is done, left and right satellites, sidelobes, replicants (bywhatever name) have identical mathematical content—one is the mirrorimage of the other with complex conjugation (Hermitian symmetry).

Therefore, it would be equivalent in B1 map synthesis to usemagnitude(2×Left), or to use magnitude(2×Right), in place of(magnitude(Left)+magnitude(Right)).

It is also now possible to use the B0 map to effect a B0 correction to aB1 map. For RF tag pulses, note that the effective strength of a squarepulse is reduced by off-resonance effects. It is possible to keep thiseffect small by using short pulse durations etc., so it may or may notbe significant. But it is also possible, once a B0 (or “off-resonance”)map is available, to directly correct for that effect, thereby improvingthe B1 map.

If, for example, one square pulse has a duration of 100 microseconds, at3 T, and a pre-pulse is applied on-resonance for water, then theuncorrected error in applied tip angle at +/−420 Hz (i.e., at fat), isabout 1.2% (at fat). Off-resonant signals experience under-tipping soone would get underestimates of the B1 map by a comparable order ofmagnitude.

In a standard linear domain approximation, and ignoring relaxation, ifone RF square pulse has the form B*rect(t/Δt), i.e., the duration of thepulse is Δt, then the tip angle on-resonance is B(Δt) and the tipoff-resonance is BΔt(sinc(ΔtΔf) or BΔt(sin(πΔtΔf))/(πΔtΔf)

-   -   where t and Δt are in seconds and Δf is in cycles/second.

Thus degradation of tip angle as a function of Δf is then:tip(Δf)/tip(onResonance)=sinc(ΔfΔt)=sin(πΔfΔt))/(πΔfΔt).

Therefore, B1 maps can be corrected:B1corr=B1uncorr/sinc(ΔfΔt) and Δf is the result, in Hz, from the B0 map.

Extension of these methods to 3-D mapping is limited by the persistenceof previous tags. Simplistic multislice interleaving fails, since alltag pre-pulses project through the whole volume. A 3-D application mayneed either TR>T1 with no interleaving or a true 3-D single-shotreadout.

While certain embodiments of the invention have been described, theseembodiments have been presented by way of example only, and are notintended to limit the scope of the invention. Indeed, the novel methodsand systems described herein may be embodied in a variety of otherforms; furthermore, various omissions, substitutions and changes in theform of the methods and systems described herein may be made withoutdeparting from the spirit of the invention. The accompanying claims andtheir equivalents are intended to cover such forms or modifications aswould fall within the scope and spirit of the invention.

What is claimed is:
 1. A method for generating a B0 map in an MRIsystem, said method comprising using an MRI system to: (a) acquire atleast one set of amplitude tagged MRI data signals in spatial frequencydomain k-space from MR nuclei within an imaged volume of the MRI system;(b) process said k-space data with at least one data processor in orderto produce at least two sub-sets of frequency-filtered k-space dataincluding at least two of: (i) a baseline low-frequency sub-set, (ii) apositive higher frequency sub-set including a harmonic version of saidbaseline sub-set, and (iii) a negative higher frequency sub-setincluding a harmonic version of said baseline sub-set; (c) separatelyFourier transform each of said at least two sub-sets in order to produceat least two respectively corresponding complex-valued spatial domaindata sets; (d) arithmetically combine said at least two complex-valuedspatial domain data sets on a pixel-by-pixel basis in order to generateand provide an off-resonance phase set of pixel data representing a B0map value; and (e) store said B0 map values in a non-transitory computeraccessible and readable memory device that is subsequently usable bysaid MRI system.
 2. A method for generating a B0 map as in claim 1,wherein step (d) comprises: calculating a difference value between thecomplex phases of said at least two complex-valued spatial domain datasets on a pixel-by-pixel basis in order to generate and provide anoff-resonance phase set of pixel data representing a B0 map value.
 3. Amethod for generating a B0 map as in claim 2, wherein said at least twocomplex-valued spatial domain data sets comprise: (i) a 2DFT of saidbaseline low-frequency sub-set, and (ii) a 2DFT of one of said positiveand negative higher frequency sub-sets.
 4. A method for generating a B0map as in claim 2, wherein said at least two complex-valued spatialdomain data sets comprise: (i) a 2DFT of said positive higher frequencysub-set and (ii) a 2DFT of said negative higher frequency sub-set.
 5. Amethod for generating a B0 map as in claim 1, wherein said sub-sets offrequency-filtered k-space data comprise windowed k-space data fromsubstantially equally-sized windows.
 6. A method for generating a B0 mapas in claim 5, wherein each of said windows comprises no more thanone-third of k-space data.
 7. A method for generating a B0 map as inclaim 1, and further comprising: generating a B1 map using at least twoof said sub-sets of frequency-filtered k-space data; and correcting saidB1 map using said B0 map.
 8. A method for generating a B0 map as inclaim 1, wherein said amplitude tagged MRI data signals are generatedusing phase-cycled tagging pulse pairs, wherein the polarity of an RFtag pulse is reversed in one pair of tagging pulses as compared toanother pair of tagging pulses, thereby improving the selectivity ofsignals appearing in said frequency-filtered k-space data.
 9. Anon-transitory computer-readable storage medium containing computerprogram code which, when executed, effects the method of claim
 1. 10. AnMRI system comprising: an MRI scanner configured to acquire at least oneset of amplitude tagged MRI data signals in spatial frequency domaink-space from MR nuclei within an imaged volume of the MRI system; and atleast one processor configured to: process said k-space data in order toproduce at least two sub-sets of frequency-filtered k-space dataincluding at least two of: (i) a baseline low-frequency sub-set, (ii) apositive higher frequency sub-set including a harmonic version of saidbaseline sub-set, and (iii) a negative higher frequency sub-setincluding a harmonic version of said baseline sub-set; separatelyFourier transform each of said at least two sub-sets in order to produceat least two respectively corresponding complex-valued spatial domaindata sets; arithmetically combine said at least two complex-valuedspatial domain data sets on a pixel-by-pixel basis in order to generateand provide an off-resonance phase set of pixel data representing a B0map value; and store said B0 map values in a non-transitory computeraccessible and readable memory device for subsequent use by said MRIsystem.
 11. An MRI system as in claim 10, wherein said arithmeticcombination comprises: calculating a phase difference value between saidat least two complex-valued spatial domain data sets on a pixel-by-pixelbasis in order to generate and provide an off-resonance phase set ofpixel data representing a B0 map value.
 12. An MRI system as in claim11, wherein said at least two complex-valued spatial domain data setscomprise (i) a 2DFT of said baseline low-frequency sub-set, and (ii) a2DFT of one of said positive and negative higher frequency sub-sets. 13.An MRI system as in claim 11, wherein said at least two complex-valuedspatial domain data sets comprise (i) a 2DFT of said positive higherfrequency sub-set, and (ii) a 2DFT of said negative higher frequencysub-set.
 14. An MRI system as in claim 10, wherein said sub-sets offrequency-filtered k-space data comprise windowed k-space data fromsubstantially equally-sized windows.
 15. An MRI system as in claim 14,wherein each of said windows comprises no more than one-third of k-spacedata.
 16. An MRI system as in claim 10 and further configured to:generate a B1 map using at least two of said sub-sets offrequency-filtered k-space data; and correct said B1 map using said B0map.
 17. An MRI system as in claim 10, wherein said amplitude tagged MRIdata signals are generated using phase-cycled tagging pulse pairs,wherein the polarity of an RF tag pulse is reversed in one pair oftagging pulses as compared to another pair of tagging pulses, therebyimproving the selectivity of signals appearing in saidfrequency-filtered k-space data.